Quantum-entanglement is a phenomenon in which the quantum states of two objects (e.g. photons or electrons) become correlated and remain correlated even when the objects are separated from each other. Subsequent measurements of a previously indeterminate quantum state of one object will be correlated to a subsequent measurement of the second object.
Light beams with quantum-entanglement have value as a tool for studying quantum fields, making precise measurements, writing sub wavelength spatial structures (for example in photolithography) and for quantum information and communication protocols (including quantum-encryption). See generally: P. D. Drummond and Z. Ficek, Quantum Squeezing (Springer, Berlin) 2004); E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992); S. Schiller, R. Bruckmeier, M. Schalke, K. Schneider, and J. Mlynek, Europhys. Lett. 36, 361 (1996); P. H. S. Ribeiro, C. Schwab, A. Maître, and C. Fabre, Opt. Lett. 20, 1893 (1997); N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, Science 301, 940 (2003); A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000); S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005) all hereby incorporated by reference.
Referring to FIG. 1, a widely used approach for generating quantum-entangled light beams employs a frequency-converting optical material 10, such as a crystal with a quadratic nonlinearity, that may be pumped with photons 12 at a first frequency of 2ω to generate, in a “down-conversion” process, a pair of photons 14 and 14′ for each photon 12. The photons 14 and 14′ each have half the frequency of photon 12, that is, a frequency of ω. Importantly the two photons 14 and 14′, created from each photon 12, are quantum-entangled 16.
Higher frequency quantum-entangled light with shorter wavelengths, can be particularly important for applications involving measurements, imaging (including lithography) and communications, yet this down-conversion process may be disadvantageous when high frequency quantum-entangled light beams are desired. The input photons 12 of the light used for pumping the optical material 10 must, in the down-converting system, have twice the frequency of the light to be produced. Such high frequency input light may be difficult or inefficient to generate and may not provide good conversion efficiencies with common down-converting optical materials 10.
Referring to FIG. 2, an up-conversion process is also known where two photons 20 and 20′ of frequency ω are received by the optical material 10 to generate a single photon 24 of twice the frequency, that is, 2ω. Referring to FIG. 3, two up-converted beams of photons 24, for example, from lasers 26 and 26′ may be quantum-entangled by directing them to opposite sides of a beam splitter 36. Specifically, separate optical material 10 and 10′ for each laser 26 and 26′ may receive a pumping beam of photons 20 and 20′ derived from a single source 30 split by beam splitter 32 and then directed to the optical material 10 and 10′ respectively, by diverting mirrors 22 and 22′. As before, each beam of photons may have a frequency of ω and may be up-converted within the optical material 10 and 10′ to produce output beams of photons 24 and 24′ of frequency 2ω. These separate beams of photons 24 and 24′ are directed (with a precise relative phase) obliquely at opposite sides of a beam splitter 36 to generate a quantum-entanglement 16 between reflected and transmitted beams 38 and 38′.
Unlike the down-conversion process, this up-conversion process is relatively complex involving multiple optical cavities, beam splitters, combining mirrors, and optical paths that must be carefully controlled. The up-conversion process also produces output beams that have highly-squeezed states that may not be ideal for many applications. A squeezed state is one in which the product of the variance of the amplitude and phase quadratures of the light are equal to or greater than the quantum mechanical limit set by the Heisenberg uncertainty principle, yet either the amplitude or the phase quadrature has a variance which is less than the square root of this Heisenberg limit.